Development of Nonlinear Bump Stiffness Model and its Effect on Structural Stiffness and Nonlinear Rotordynamic Characteristic

Bump foils are the most frequently used in foil bearings, but the behavior of bump foils is complicated, and their characteristics have been the subject of research for decades. Bump foils are typically modeled as stiffness elements and damping through frictions with other components. In this paper, the nonlinear stiffness of bump foils in flat configuration has been experimentally measured and compared with various analytical models. These nonlinear characteristics of the bump foil of radial foil bearings can be observed during both manufacturing and operational stages because of their inherent structural properties such as bump geometry, forming process, and complicated contact behavior with bearing housing. These nonlinear characteristics of the bump foils are one of the challenges in analyzing the characteristics of the foil bearings. Furthermore, the same bump geometry but with a curved configuration for actual radial foil bearings was used to measure the structural non-linear stiffness in the bearing level in push-pull set up and compared with analytical prediction. Finally, the non-linear bump stiffness model was adopted to the radial foil bearing to calculate overall bearing stiffness and damping coefficients, and stability characteristics through modal analysis and transient time domain orbit simulations. Lastly, the nonlinear stiffness model of the bump foils will be verified by measuring bearing coefficients using shaker systems.